Saturation and beating of coherent acoustic phonon (CAP) oscillations were observed and attributed to the screening of a built-in electric field with increasing pump power using degenerate pump–probe measurements near the exciton resonance of polar ZnO/Zn0.8Mg0.2O multiple quantum wells (MQWs). After purifying the CAP signals by using an empirical mode decomposition, we found not only that the CAP amplitude follows the trend of the band gap renormalization (BGR) and shows saturation at high pump power, but also that the CAP oscillation period coincides with that of the MQWs, consistent with the XRD and TEM results. An additional low-frequency oscillation modifying the CAP signal is revealed due to the negative change in refractive index caused by BGR as the pump power increases.